Theorems · Theorem · sequences and series
tprod_one_add_ne_zero_of_summable
∀ {ι : Type u_1} {R : Type u_2} [inst : NormedCommRing R] [NormOneClass R] {f : ι → R} [CompleteSpace R]
[NormMulClass R], (∀ (i : ι), 1 + f i ≠ 0) → (Summable fun x => ‖f x‖) → ∏' (i : ι), (1 + f i) ≠ 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumproof · cited by 1,148
- Real.logproof · cited by 939
- Summablestatement and proof · cited by 778
- tprodstatement · cited by 230
- NormedCommRingstatement and proof · cited by 218
- norm_pos_iffproof · cited by 168
- NormOneClassstatement and proof · cited by 136
- NormMulClassstatement and proof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- ModularForm.eta_tprod_ne_zeroproof · cited by 2